To determine the area of the book’s cover, we need to use the relationship between force, pressure, and area. The basic formula that relates these quantities is:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
We can rearrange this formula to solve for the area:
[tex]\[ \text{Area} = \frac{\text{Force}}{\text{Pressure}} \][/tex]
Given:
- The force exerted by the book (F) is 15.0 N.
- The pressure exerted by the book (P) is 16.5 Pa.
Now, using the formula:
[tex]\[ \text{Area} = \frac{15.0 \, \text{N}}{16.5 \, \text{Pa}} \][/tex]
Performing the division:
[tex]\[ \text{Area} = \frac{15.0}{16.5} \][/tex]
This simplifies to approximately:
[tex]\[ \text{Area} \approx 0.9090909090909091 \, \text{m}^2 \][/tex]
Now we look at the given options:
1. [tex]\( 0.34 \, \text{m}^2 \)[/tex]
2. [tex]\( 0.91 \, \text{m}^2 \)[/tex]
3. [tex]\( 0.83 \, \text{m}^2 \)[/tex]
4. [tex]\( 0.22 \, \text{m}^2 \)[/tex]
Comparing our calculated result of approximately 0.91 [tex]\( \text{m}^2 \)[/tex] with the provided options, the closest value is:
[tex]\[ \boxed{0.91 \, \text{m}^2} \][/tex]
Therefore, the area of the book's cover is [tex]\( \boxed{0.91 \, \text{m}^2} \)[/tex].
